To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .

To send content to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services.
Please confirm that you accept the terms of use.

In this paper we give two different proofs that the flat cover conjecture is true: that is, every module
has a flat cover. The two proofs are of completely different nature, and, we hope, will have different
applications. The first of the two proofs (due to the third author) is essentially an application of the
work of P. Eklof and J. Trlifaj (work which is more set-theoretic). The second proof (due to the first two
authors) is more direct, and has a model-theoretic flavour.

We prove that the fundamental group of the double of the figure-eight knot exterior admits a faithful
discrete representation into SO(4,1; R), for which the image group is separable on its geometrically finite
subgroups.

The asymptotic probability theory of conjugacy classes of the finite general groups leads to a
probability measure on the set of all partitions of natural numbers. A simple method of understanding
these measures in terms of Markov chains is given in this paper, leading to an elementary probabilistic
proof of the Rogers–Ramanujan identities. This is compared with work on the uniform measure. The
main case of Bailey's lemma is interpreted as finding eigenvectors of the transition matrix of a Markov
chain. It is shown that the viewpoint of Markov chains extends to quivers.

The paper studies an isoperimetric problem for the Gaussian measure and coordinatewise symmetric
sets. The notion of boundary measure corresponding to the uniform enlargement is considered, and it is
proved that symmetric strips or their complements have minimal boundary measure.

The aim of this paper is to study properties of sequences that are recursively defined by a linear
equation and their applications to the truncated moment problem in connection with the problem of
subnormal completion of the truncated weighted shifts. Special cases are considered and some classical
results due to Stampfli, Curto and Fialkow are recovered using elementary techniques.

In this paper, a new approach to the Calabi–Bernstein theorem on maximal surfaces in the Lorentz–
Minkowski space L3 is introduced. The approach is based on an upper bound for the total curvature of
geodesic discs in a maximal surface in L3, involving the local geometry of the surface and its hyperbolic
image. As an application of this, a new proof of the Calabi–Bernstein theorem is provided.

A mean-value theorem, an inverse mapping theorem and an implicit mapping theorem are established
here in a class of complex locally convex spaces, including the spaces of test functions in distribution
theory. Our main tool is the integral formula and the invariance of the domain, derived from topological
degrees, rather than from fixed points of contractions in Banach spaces.